Problem: Simplify the following expression: $y = \dfrac{q^2 - 15q + 54}{q - 6} $
First factor the polynomial in the numerator. $ q^2 - 15q + 54 = (q - 6)(q - 9) $ So we can rewrite the expression as: $y = \dfrac{(q - 6)(q - 9)}{q - 6} $ We can divide the numerator and denominator by $(q - 6)$ on condition that $q \neq 6$ Therefore $y = q - 9; q \neq 6$